Accurate evaluation of a polynomial and its derivative in Bernstein form

Authors:
Hao Jiang;Shengguo Li;Lizhi Cheng;Fang Su
Affiliations:
School of Science, National University of Defense Technology, Changsha, 410073, China;School of Science, National University of Defense Technology, Changsha, 410073, China;School of Science, National University of Defense Technology, Changsha, 410073, China;School of Science, National University of Defense Technology, Changsha, 410073, China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In computer aided geometric design a polynomial is usually represented in Bernstein form. This paper presents two compensated algorithms to accurately evaluate a polynomial and its derivative in Bernstein form with floating point coefficients. The principle is to apply error-free transformation to improve traditional de Casteljau algorithm. Forward error analysis and numerical experiments illustrate the accuracy of our algorithms.